Standard error of mean (SEM) is used to estimate the sample mean dispersion from the population mean. The standard error along with sample mean is used to estimate the approximate confidence intervals for the mean. It is also known as standard error of mean or measurement often denoted by SE, SEM or SE.
Examples:
Input : arr[] = {78.53, 79.62, 80.25, 81.05, 83.21, 83.46}
Output : 0.8063
Input : arr[] = {5, 5.5, 4.9, 4.85, 5.25, 5.05, 6.0}
Output : 0.1546
Sample mean
Sample Standard Deviation
Estimate standard error of mean
Explanation:
given an array arr[] = {78.53, 79.62, 80.25, 81.05, 83.21, 83.46} and the task is to find standard error of mean.
mean = (78.53 + 79.62 + 80.25 + 81.05 + 83.21 + 83.46) / 6
= 486.12 / 6
= 81.02Sample Standard deviation = sqrt((78.53 – 81.02)2 + (79.62- 81.02)2 + . . . + (83.46 – 81.02)2 / (6 – 1))
= sqrt(19.5036 / 5)
= 1.97502Standard error of mean = 1.97502 / sqrt(6)
= 0.8063
C++
// C++ Program to implement // standard error of mean.#include <bits/stdc++.h>using namespace std;// Function to find sample mean.float mean(float arr[], int n){ // loop to calculate // sum of array elements. float sum = 0; for (int i = 0; i < n; i++) sum = sum + arr[i]; return sum / n;}// Function to calculate sample// standard deviation.float SSD(float arr[], int n){ float sum = 0; for (int i = 0; i < n; i++) sum = sum + (arr[i] - mean(arr, n)) * (arr[i] - mean(arr, n)); return sqrt(sum / (n - 1));}// Function to calculate sample error.float sampleError(float arr[], int n){ // Formula to find sample error. return SSD(arr, n) / sqrt(n);}// Driver functionint main(){ float arr[] = { 78.53, 79.62, 80.25, 81.05, 83.21, 83.46 }; int n = sizeof(arr) / sizeof(arr[0]); cout << sampleError(arr, n); return 0;} |
Java
// Java Program to implement// standard error of mean.class GFG { // Function to find sample mean. static float mean(float arr[], int n) { // loop to calculate // sum of array elements. float sum = 0; for (int i = 0; i < n; i++) sum = sum + arr[i]; return sum / n; } // Function to calculate sample // standard deviation. static float SSD(float arr[], int n) { float sum = 0; for (int i = 0; i < n; i++) sum = sum + (arr[i] - mean(arr, n)) * (arr[i] - mean(arr, n)); return (float)Math.sqrt(sum / (n - 1)); } // Function to calculate sample error. static float sampleError(float arr[], int n) { // Formula to find sample error. return SSD(arr, n) / (float)Math.sqrt(n); } // Driver function public static void main(String[] args) { float arr[] = { 78.53f, 79.62f, 80.25f, 81.05f, 83.21f, 83.46f }; int n = arr.length; System.out.println(sampleError(arr, n)); }}// This code is contributed // by prerna saini |
Python3
# Python 3 Program to implement # standard error of mean.import math# Function to find sample mean.def mean(arr, n) : # loop to calculate # sum of array elements. sm = 0 for i in range(0,n) : sm = sm + arr[i] return sm / n# Function to calculate sample# standard deviation.def SSD(arr, n) : sm = 0 for i in range(0,n) : sm = sm + (arr[i] - mean(arr, n)) * (arr[i] - mean(arr, n)) return (math.sqrt(sm / (n - 1))) # Function to calculate sample error.def sampleError(arr, n) : # Formula to find sample error. return SSD(arr, n) / (math.sqrt(n)) # Driver functionarr = [ 78.53, 79.62, 80.25, 81.05, 83.21, 83.46]n = len(arr)print(sampleError(arr, n)) # This code is contributed# by Nikita Tiwari. |
C#
// C# Program to implement// standard error of mean.using System;class GFG { // Function to find sample mean. static float mean(float []arr, int n) { // loop to calculate // sum of array elements. float sum = 0; for (int i = 0; i < n; i++) sum = sum + arr[i]; return sum / n; } // Function to calculate sample // standard deviation. static float SSD(float []arr, int n) { float sum = 0; for (int i = 0; i < n; i++) sum = sum + (arr[i] - mean(arr, n)) * (arr[i] - mean(arr, n)); return (float)Math.Sqrt(sum / (n - 1)); } // Function to calculate sample error. static float sampleError(float []arr, int n) { // Formula to find sample error. return SSD(arr, n) / (float)Math.Sqrt(n); } // Driver code public static void Main() { float []arr = {78.53f, 79.62f, 80.25f, 81.05f, 83.21f, 83.46f}; int n = arr.Length; Console.Write(sampleError(arr, n)); }}// This code is contributed by Nitin Mittal. |
PHP
<?php// PHP Program to implement // standard error of mean.// Function to find sample mean.function mean($arr,$n){ // loop to calculate // sum of array elements. $sum = 0; for ($i = 0; $i < $n; $i++) $sum = $sum + $arr[$i]; return $sum / $n;}// Function to calculate sample// standard deviation.function SSD($arr, $n){ $sum = 0; for ($i = 0; $i < $n; $i++) $sum = $sum + ($arr[$i] - mean($arr, $n)) * ($arr[$i] - mean($arr, $n)); return sqrt($sum / ($n - 1));}// Function to calculate// sample error.function sampleError($arr, $n){ // Formula to find sample error. return SSD($arr, $n) / sqrt($n);}// Driver Code{ $arr = array(78.53, 79.62, 80.25, 81.05, 83.21, 83.46 ); $n = sizeof($arr) / sizeof($arr[0]); echo sampleError($arr, $n); return 0;}// This code is contributed by nitin mittal.?> |
JavaScript
<script>// JavaScript Program to implement// standard error of mean.// Function to find sample mean.function mean(arr, n){ // loop to calculate // sum of array elements. let sm = 0 for (var i = 0; i < n; i++) sm = sm + arr[i] return sm / n}// Function to calculate sample// standard deviation.function SSD(arr, n){ let sm = 0 for (var i = 0; i < n; i++) sm = sm + (arr[i] - mean(arr, n)) * (arr[i] - mean(arr, n)) return (Math.sqrt(sm / (n - 1)))}// Function to calculate sample error.function sampleError(arr, n) { // Formula to find sample error. return SSD(arr, n) / (Math.sqrt(n))}// Driver functionlet arr = [ 78.53, 79.62, 80.25, 81.05, 83.21, 83.46]let n = arr.lengthconsole.log(sampleError(arr, n)) // This code is contributed by phasing17</script> |
Output
0.8063
Time Complexity: O(N2), for calculation of mean N times while calculating Sample Standard Deviation.
Auxiliary Space: O(1), as constant extra space is required.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
